Jammed disks in a narrow channel: criticality and ordering tendencies

Abstract

Abstract. A system of identical disks is confined to a narrow channel, closed off at one end by a stopper and at the other end by a piston. All surfaces are hard and frictionless. A uniform gravitational field is directed parallel to the plane of the disks and perpendicular to the axis of the channel. We employ a method of configurational statistics that interprets jammed states as configurations of floating particles with structure. The particles interlink according to set rules. The two jammed microstates with smallest volume act as pseudo-vacuum. The placement of particles is subject to a generalized Pauli principle. Jammed macrostates are generated by random agitations and specified by two control variables. They are inferred from measures for expansion work against the piston, gravitational potential energy, and intensity of random agitations. In this two-dimensional space of variables there exists a critical point. The jammed macrostate realized at the critical point depends on the path of approach. We describe all jammed macrostates by volume and entropy. Both are functions of the average population densities of particles. Approaching the critical point in an extended space of control variables generates two types of jammed macrostates: states with random heterogeneities in mass density and states with domains of uniform mass density. Criticality is shown to be robust against some effects of friction.

Interacting hard rods on a lattice: Distribution of microstates and density functionals

“…3 were recently found by a study of jammed granular matter in a narrow channel. 52 A point of some interest is the location of the entropy maximum in dependence of σ and v c (first maximum for v c > v c in the case of repulsive interactions). The curves show that for v c = 0 the coverage of maximum entropy shifts to right from ρ = 1/2 as the size of the rods grows from σ = 1 and that, for given σ > 1, it shift to left as |v c | increases.…”

Inherent structures, fragility, and jamming: Insights from quasi-one-dimensional hard disks

“…In the context of understanding athermal granular systems, a knowledge of the ensemble of jammed states is of considerable interest to the development of a granular statistical mechanics [36], and the current model has been used to test ideas relating to temperaturelike thermodynamic quantities such as the compactivity [37][38][39][40].…”

Disks in a narrow channel jammed by gravity and centrifuge: profiles of pressure, mass density and entropy density

“…The adaptation to jammed granular matter as reported in Ref. [23] is embedded in the framework of configurational statistics [39,40].…”

“…in generalization of the zero-gravity situation [23]. Equations (7) with (11) used on the left are valid on a mesoscopic scale with the z-axis pointing vertically down and z = 0 located at the top of the pile of disks.…”